I actually asked this exact same question a couple of years ago! Glad you brought it up again...
My two cents:
La Villa...3632 N. Pulaski....very near Sabatinos.....great old bar...Cheesy accordian player to boot in the bar...cheap, cheap drinks too! Great food....amazingly friendly staff (see profile on Check Please site). And sacrilege of sacrileges...there are times we actually prefer this to Sabatinos.....
some times...
Ambrogio...6706 W. Belmont....a real hole in the wall locals place....a little scruffy, but perfectly fine....you really feel like you've discovered something nobody outside the neighborhood knows about..
The Playroom...7958 W. Belmont....not really old, but feels like it....again, real locals kind of place.....you expect Paulie Walnuts to pop through the door at any second....again, very nice, very Italian staff...bonus.....free sausage and peppers and ribs during the Bears games
Colletti's...5707 N. Central. Will food blow you away...no...but it's pretty darn decent (linguine with clams are great)..pizza certainly good as well...eat at the bar and watch the old timers sing Karaoke on weekends. Again, lovely service...
Again, none of the above approaches Sabatinos in terms of overal food quality (and in terms of some of the amusingly borderline personality disorders of some of the wait staff....and I say that with all affection)....but they are nice options not far away when you crave that old Chicago Italian-American vibe.